Mechanism of high-preload support based on the NPR anchor cable in layered soft rock tunnels

The control of large deformation problems in layered soft rock tunnels needs to solve urgently.The roof problem is particularly severe among the deformation issues in tunnels.This study first analyzes the asymmetric deformation modes in layered soft rock tunnels with large deformations.Subsequently,we construct a mechanical model under ideal conditions for controlling the roof of layered soft rock tunnels through high preload with the support of NPR anchor cables.The prominent roles of long and short NPR anchor cables in the support system are also analyzed.The results indicate the significance of high preload in controlling the roof of layered soft rock tunnels.The short NPR anchor cables effectively improve the integrity of the stratified soft rock layers,while the long NPR anchor cables effectively mobilize the self-bearing capacity of deep-stable rock layers.Finally,the high-preload support method with NPR anchor cables is validated to have a good effect on controlling large deformations in layered soft rock tunnels through field monitoring data.

Case study on the mechanics of NPR anchor cable compensation for large deformation tunnel in soft rock in the Transverse Mountain area,China

A study was conducted to analyze the deformation mechanism of strongly weathered quartz schist in the Daliangshan Tunnel,located in the western Transverse Mountain area.A large deformation problem was experienced during the tunnel construction.To mitigate this problem,a support system was designed incorporating negative Poisson ratio(NPR)anchor cables with negative Poisson ratio effect.Physical model experiments,field experiments,and numerical simulation experiments were conducted to investigate the compensation mechanical behavior of NPR anchor cables.The large deformations of soft rocks in the Daliangshan Tunnel are caused by a high ground stress,a high degree of joint fracture development,and a high degree of surrounding rock fragmentation.A compensation mechanics support system combining long and short NPR anchor cables was suggested to provide sufficient counter-support force(approximately 350 kN)for the surrounding rock inside the tunnel.Comparing the NPR anchor cable support system with the original support system used in the Daliangshan tunnel showed that an NPR anchor cable support system,combining cables of 6.3 m and 10.3 m in length,effectively prevented convergence of surrounding rock deformation,and the integrated settlement convergence value remained below 300 mm.This study provides an effective scientific basis for resolving large deformation problems in deeply buried soft rocks in western transverse mountain areas.

Mechanical behavior of 2G NPR bolt anchored rock samples under static disturbance loading

The deep mining of coal resources is accompanied by severe environmental challenges and various potential engineering hazards.The implementation of NPR(negative Poisson's ratio)bolts are capable of controlling large deformations in the surrounding rock effectively.This paper focuses on studying the mechanical properties of the NPR bolt under static disturbance load.The deep nonlinear mechanical experimental system was used to study the mechanical behavior of rock samples with different anchored types(unanchored/PR anchored/2G NPR anchored)under static disturbance load.The whole process of rock samples was taken by high-speed camera to obtain the real-time failure characteristics under static disturbance load.At the same time,the acoustic emission signal was collected to obtain the key characteristic parameters of acoustic emission such as acoustic emission count,energy,and frequency.The deformation at the failure of the samples was calculated and analyzed by digital speckle software.The findings indicate that the failure mode of rock is influenced by different types of anchoring.The peak failure strength of 2G NPR bolt anchored rock samples exhibits an increase of 6.5%when compared to the unanchored rock samples.The cumulative count and cumulative energy of acoustic emission exhibit a decrease of 62.16%and 62.90%,respectively.The maximum deformation of bearing capacity exhibits an increase of 59.27%,while the failure time demonstrates a delay of 42.86%.The peak failure strength of the 2G NPR bolt anchored ones under static disturbance load exhibits an increase of 5.94%when compared to the rock anchored by PR(Poisson's ratio)bolt.The cumulative count and cumulative energy of acoustic emission exhibit a decrease of 47.16%and 43.86%,respectively.The maximum deformation of the bearing capacity exhibits an increase of 50.43%,and the failure time demonstrates a delay of 32%.After anchoring by 2G NPR bolt,anchoring support effectively reduces the risk of damage caused by static disturbance load.These results demonstrate that the support effect of 2G NPR bolt materials surpasses that of PR bolt.

穿断层隧道NPR锚索支护体系抗震特性振动台试验研究

为研究具有负泊松比效应(negative Poisson’s ratio,NPR)的恒阻大变形锚索在地震作用下的吸能特性与动力响应规律,利用振动台开展含断层隧道使用普通锚索支护以及使用NPR锚索支护的振动台物理模型试验,对比分析地震作用下处于不同围岩条件中以及使用不同锚索进行支护时隧道结构的动力响应规律。研究结果表明:在同一地震波作用下,使用NPR锚索进行支护的隧道结构破坏程度与使用普通锚索进行支护的隧道结构相比有明显的改善,表明NPR锚索在地震作用下具有良好的吸能特性,能够为隧道结构提供有效支护;通过对比分析普通锚索与NPR锚索的锚索轴力时程曲线可知,在地震波作用下,普通锚索会发生破断现象,轴力突降至零,而NPR锚索的高恒阻力能够持续提供有效支护;分析隧道结构各测点的加速度、应变、土压力等动力响应可知,隧道断层区域在地震作用下的动力响应更为明显,隧道结构在地震作用下呈现出拱肩→拱腰→拱顶的破坏规律,这一研究成果为类似隧道工程的支护对策提供了理论参考。

降雨诱发滑坡的NPR锚索控制机理及临滑预警

为研究降雨滑坡的控制及临滑预警技术,以熊家山滑坡为原型,通过分析边坡变形的时空特征,设计了相似模型试验.以普通预应力锚索(简称PR锚索)和NPR锚索为加固材料,运用高速摄像机、孔压、土压和锚索力传感器,分析了降雨诱发的滑坡规律和锚索控制机理,并结合现场试验探究了滑坡牛顿力变化规律.结果表明:孔隙水压力突降与边坡局部滑塌近似同步;NPR锚索力突降,边坡内部产生局部变形;PR锚索因无法承受大变形被拉断失效,而NPR锚索凭借恒阻大变形特性产生高应力吸能控制功能,促使边坡达到二次平衡状态;NPR锚索在滑坡前表现出明显的“先突增,后突降”的变形-临滑动力学规律;现场试验揭示了滑坡全过程牛顿力演变规律,提前7.5 h发出临滑预警.

Strength characteristics of rock anchored by NPR bolt with different preloads

This study compares the strength characteristics of rocks anchored by NPR bolts and ordinary bolts with varied preloads,based on the mechanical properties of NPR bolts(with a negative Poisson’s ratio).The results show that the uniaxial compressive stress-strain curve of ordinary anchored rocks exhibits noticeable abrupt changes.After reaching peak strength,the bolt breaks,whereas the stress-strain curve of NPR-anchored rocks is smoother.The NPR bolt enters the stage of continuous resistance after reaching maximal strength and does not break.As the preload increases,the strength of the anchored rock grows linearly.A calculation equation for the strength of the anchored rock is proposed based on the preload.The theoretical equation fits the test results well,and the fitted parameters show that NPR bolts can better increase the strength of the rock.The concept of dynamic toughness UC of anchored rock is proposed to reflect the comprehensive mechanical properties of anchored rock,including strength and plasticity.As the preload increases,the UC of ordinary anchored rock first decreases and then increases,while the UC of the NPR anchored rock does not change significantly with the preload when the strain is small,and the UC increases with the increase of the preload when the strain is large.

Instability mechanism of mining roadway passing through fault at different angles in kilometre-deep mine and control measures of roof cutting and NPR cables

The angle α between the fault strike and the axial direction of the roadway produces different damage characteristics. In this paper, the research methodology includes theoretical analyses, numerical simulations and field experiments in the context of the Daqiang coal mine located in Shenyang, China. The stability control countermeasure of "pre-splitting cutting roof + NPR anchor cable"(PSCR-NPR) is simultaneously proposed. According to the different deformation characteristics of the roadway, the faults are innovatively classified into three types, with α of type I being 0°-30°, α of type II being 30°-60°, and α of type III being 60°-90°. The full-cycle stress evolution paths during mining roadway traverses across different types of faults are investigated by numerical simulation. Different pinch angles α lead to high stress concentration areas at different locations in the surrounding rock. The non-uniform stress field formed in the shallow surrounding rock is an important reason for the instability of the roadway. The pre-cracked cut top shifted the high stress region to the deep rock mass and formed a low stress region in the shallow rock mass. The high prestressing NPR anchor cable transforms the non-uniform stress field of the shallow surrounding rock into a uniform stress field. PSCR-NPR is applied in the fault-through roadway of Daqiang mine. The low stress area of the surrounding rock was enlarged by 3-7 times, and the cumulative convergence was reduced by 45%-50%. It provides a reference for the stability control of the deep fault-through mining roadway.

Negative Poisson's ratio and peripheral strain of an NPR anchor cable

Materials with a negative Poisson’s ratio effect perform significantly better than traditional materials for rock mass impact resistance,shear resistance,and energy absorption.Based on these advantages,a negative Poisson’s ratio anchor cable(NPR anchor cable)with high elongation and constant resistance was developed and successfully applied in the field of mine disaster control.However,theoretical and experimental research on the negative Poisson’s ratio effect and peripheral strain characteristics of NPR anchor cables is currently incomplete.This study used several theories and methods,such as static tensile,peripheral strain measurement,and static negative Poisson’s ratio measurement,to investigate the radial deformation law of an NPR anchor cable and the negative Poisson’s ratio characteristics.Experimental results elucidated constant resistance changes in an NPR anchor cable during operation,the motion of the constant resistance body in the constant resistance sleeve,and the deformation law of the constant resistance sleeve.Negative Poisson’s ratio characteristics of the NPR anchor cable and its superior energy absorption characteristics were verified and it provided a theoretical and experimental basis for energy absorption mechanisms of an NPR anchor cable.

NPR钢板材多性能试验研究

开展NPR钢主要力学性能试验研究,并将其相关性能与舰用921A钢进行对比。结果表明:NPR钢具备较高的拉伸强度,同时还保持着优异的韧性,其面内方向吸收能量的能力较强;在高应变速率条件下,NPR钢的屈服强度和极限强度均有较大提高,表现出较强的应变率敏感性。此外,NPR钢材的耐腐蚀性能、冷弯曲加工性能和低磁/无磁性能均表现优异。研究结果表明:NPR钢的综合性能较好,尤其适合应用于对大变形、高应力和高延性有较高要求的工程场景,在舰船抗爆和抗冲击等领域有较好的应用预期。

万福矿深埋大断面T型交叉点高预应力NPR支护机制及应用

为解决深部大断面软岩巷道交叉点大变形问题,以万福煤矿千米深井巷道交叉点为工程实例,首次在巷道支护中运用微观负泊松比(negative Poisson’s ration,NPR)钢锚索。采用室内试验、理论分析、数值模拟及现场试验相结合的方法,分析了深埋巷道交叉点的围岩变形机制,提出了以微观NPR钢锚索为核心的控制对策。通过室内静力拉伸试验对微观NPR钢锚索的力学特性进行研究,结果表明,微观NPR钢锚索拉伸全过程表现为高恒阻,均匀拉伸,无屈服平台,破断时无明显颈缩现象。通过理论推导,基于T型巷道交叉点围岩最大影响范围,建立微观NPR钢锚索支护T型巷道交叉口最大影响范围计算模型。通过数值模拟,再现T型巷道交叉口的破坏演化过程,分析对比普通支护/微观NPR钢锚索支护效果。现场开展支护应用试验与监测,验证了长短微观NPR钢锚索联合支护对策具有良好的交叉口围岩大变形控制效果,为交叉口围岩安全稳定控制提供了新支护材料和支护手段。

引汉济渭工程秦岭引水隧洞岩爆三维NPR支护技术

针对引汉济渭工程秦岭引水隧洞岭北段频繁产生岩爆灾害、原支护结构破坏等问题,对秦岭引水隧洞岭北段进行地质勘测调查,分析隧道围岩岩爆破坏特征及破坏模式,开展超深隧洞岩爆三维负泊松比(negative Poisson’s ration,NPR)高应力补偿支护体系研究工作。采用现场勘查等方法,对隧道地质条件及岩爆破坏成因进行分析,并采用对比试验的思想设计出秦岭引水隧洞岭北段岩爆监测预警试验方案,提出以微观NPR锚杆为核心的三维NPR高应力补偿支护体系;通过现场试验分析新支护体系下围岩岩爆控制程度及其支护效果。结果表明:以微观NPR锚杆为核心的三维NPR高应力补偿支护体系能有效控制隧道围岩岩爆灾害发生,新支护体系试验段微震能量、频次均明显降低,爆坑深度、钢拱架受力和变形量明显减小。研究成果可为超深隧道岩爆灾害的防治提供参考。

NPR锚索支护下相交隧道围岩变形规律及破坏机理

城市交通逐渐向地下发展,地下立交中相交隧道数量日益增加。为探究复杂地质条件下相交隧道的变形规律,以深圳南龙地下立交隧道相交隧道段为工程背景,通过物理模型试验探索相交隧道在开挖支护及超载状态下的变形机理。首先自主设计三维模型试验系统,并通过相似理论计算,进行了多种岩样及支护材料的配制;其次在模型搭建完成后,基于开挖补偿理论,利用缩尺NPR(Negative Poisson’s Ratio)锚索对相交隧道进行开挖支护。通过对隧道应变、位移及NPR锚索轴力的分析,得到隧道开挖状态下的应力重分布特征;最后,对隧道进行超载试验,结合数据及现象分析,揭示了相交隧道合建结构的围岩破坏机理。研究结果表明:相交隧道在开挖贯通时,合建区域岩体因隧道开挖产生应力损失,会对已经开挖支护完的隧道造成轻微影响。隧道贯通加载时,相交隧道的破坏分为3个阶段:拱顶应力集中区沉降阶段、合建结构的破坏阶段和隧道洞口破坏阶段。具体表现:首先是上层隧道合建区域拱顶开始出现沉降,然后下层隧道出现底鼓,最后应力传播至边界,使得洞口上方垮塌。试验中采用NPR锚索对相交隧道进行支护,现象和数据表明,开挖阶段隧道合建区的沉降影响到NPR支护段,由于NPR锚索的高应力补偿特点,支护段并未出现明显沉降。试验验证了NPR锚索在相交隧道的支护效果,可为类似工程支护提供一种新的思路。

Stability control measures for roof cutting and NPR supporting of mining roadways in fault areas of kilometre-deep coal mine

The study focuses on the stability control measures for mining roadways in fault zones of deep mines,using Daqiang Coal Mine as a case study.The control system under consideration,referred to as"pre-splitting cutting roof+NPR anchor cable"(PSCR-NPR),is subjected to scrutiny through theoretical analysis,numerical modelling,and field trials.Furthermore,a comprehensive analysis is undertaken to evaluate the stability control mechanism of this particular technology.The study provides evidence that the utilization of deep-hole directional energy-concentrated blasting facilitates the attainment of directional roof cutting in roadways.The aforementioned procedure leads to the formation of a uniform structural surface on the roof of the roadway and causes modifications in the surrounding geological formation.The examination of the lateral abutment pressure and shear stress distribution,both prior to and subsequent to roof cutting,indicates that the implementation of pre-splitting techniques leads to a noteworthy reduction in pressure.The proposition of incorporating the safety factor Q for roof cutting height is suggested as a method to augment comprehension of the pressure relief phenomenon in the field of engineering.The analysis of numerical simulation has indicated that the optimal pressure relief effect of a mining roadway in a fault area is attained when the value of Q is 1.8.The NPR anchor cable exhibits noteworthy characteristics,including a high level of prestress,continuous resistance,and substantial deformation.After the excavation of the roadway,a notable reduction in radial stress occurs,leading to the reinstatement of the three-phase stress state in the surrounding rock.This restoration is attributed to the substantial prestress exerted on the radial stress.The termination point of the NPR anchor cable is strategically positioned within a stable rock formation,allowing for the utilization of the mechanical characteristics of the deep stable rock mass.This positioning serves to improve the load-bearing capacity of the surrounding rock.The mining roadway within the fault region of Daqiang Coal Mine is outfitted with the PSCR-NPR technology.The drop in shear stress experienced by the rock surrounding the roadway is estimated to be around 30%,whilst the low-stress region of the mining roadway extends by a factor of approximately 5.5.The magnitude of surface displacement convergence experiences a decrease of approximately 45%-50%.The study’s findings provide useful insights regarding the stable of mining roadway in characterized by fault zones.

Model test of negative Poisson’s ratio cable for supporting super-largespan tunnel using excavation compensation method

In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult.Unfortunately,there are few studies on the failure and support mechanism of the surrounding rocks in the excavation of supported tunnel,while most model tests of super-large-span tunnels focus on the failure characteristics of surrounding rocks in tunnel excavation without supports.Based on excavation compensation method(ECM),model tests of a super-large-span tunnel excavation by different anchor cable support methods in the initial support stage were carried out.The results indicate that during excavation of super-large-span tunnel,the stress and displacement of the shallow surrounding rocks decrease,following a step-shape pattern,and the tunnel failure is mainly concentrated on the vault and spandrel areas.Compared with conventional anchor cable supports,the NPR(negative Poisson’s ratio)anchor cable support is more suitable for the initial support stage of the super-large-span tunnels.The tunnel support theory,model test materials,methods,and the results obtained in this study could provide references for study of similar super-large-span tunnels。

Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson's ratio

This paper proposes a three-dimensional(3D)Maltese cross metamaterial with negative Poisson’s ratio(NPR)and negative thermal expansion(NTE)adopted as the core layers in sandwich plates,and aims to explore the relations between the mechanical responses of sandwich composites and the NPR or NTE of the metamaterial.First,the NPR and NTE of the metamaterial are derived analytically based on energy conservation.The effective elastic modulus and mass density of the 3D metamaterial are obtained and validated by the finite element method(FEM).Subsequently,the general governing equation of the 3D sandwich plate under thermal environments is established based on Hamilton’s principle with the consideration of the von Kármán nonlinearity.The differential quadrature(DQ)FEM(DQFEM)is utilized to obtain the numerical solutions.It is shown that NPR and NTE can enhance the global stiffness of sandwich structures.The geometric parameters of the Maltese cross metamaterial significantly affect the responses of the thermal stress,natural frequency,and critical buckling load.

岩爆机制及其控制

随着岩体工程向深部发展,开挖引发的围岩大变形和强冲击诱发的动力破坏日益严峻。岩爆作为深部地下工程中常见的一种强动力灾害,被称为岩土工程界的“癌症”,其具有突发性特点,难以有效预报及防治,严重地威胁着施工人员的安全和设备的正常运行。通过对比岩石在真三轴卸荷和单轴压缩这2种应力路径下的储能差异,对岩爆多余能量机制进行探讨。首先,根据岩爆诱发机制的不同,将岩爆分为由应力集中导致的应变型岩爆和扰动诱发的冲击岩爆。然后,模拟开挖诱发的不同类型岩爆的应力路径进而在室内再现各种岩爆现象,并对其机制进行研究,自主研发3套真三轴岩爆模拟试验系统:第1代应变岩爆试验系统、第2代应变岩爆试验系统、冲击岩爆试验系统。同时,在实验室内成功模拟不同类型的岩爆:巷道应变岩爆、巷道交叉点应变岩爆、3个临空面矿柱应变岩爆、矿柱应变岩爆以及动荷载诱发的冲击岩爆。最后,为有效控制岩爆灾害,提出开挖补偿法,并研发具有负泊松比效应的宏观和微观NPR锚杆/索。工程实践证明,NPR锚杆/索能提供高预应力来补偿开挖造成的应力损失,同时具备良好的延展性和吸能效果,可为岩爆灾害的防治提供有效途径。

高地应力软岩隧道围岩大变形NPR锚索控制方法研究

为解决高地应力软岩隧道建设过程中支护结构破坏、围岩大变形等问题,依托地处炭质板岩地层,具有地质构造复杂、断层发育、埋深大、地应力极高等特点的木寨岭特长公路隧道工程,对隧道围岩NPR锚索支护方案进行研究。首先,采用原位试验、现场勘察和室内试验方法,对其地质条件及破坏成因进行分析;然后,利用自主研发的高预紧力恒阻大变形锚索(NPR锚索)材料,设计出一种能够控制公路隧道围岩大变形的NPR锚索综合控制体系;最后,使用该控制体系在现场进行工业性试验,通过对NPR锚索加固区的围岩变形量、钢拱架应力和NPR锚索受力进行实时监测,分析NPR锚索支护方案的围岩控制效果。试验结果表明:采用NPR锚索“非对称布设和长-短锚索组合搭配”的综合控制体系,能有效控制隧道围岩初期支护大变形难题,最大变形量从2936 mm控制到240 mm以内,消除了初期支护侵限、开裂等破坏隐患,控制效果显著。

缓凝型水泥浆液配合比优化及锚孔浆岩界面特性影响研究

针对预应力锚杆后张法施工中自由段浆液流动性和缓凝效果差的工程难题,提出使用标准型聚羧酸减水剂作为掺加剂以实现水泥浆液缓凝并提高其工作性能,探究其对锚孔浆岩界面特性的影响。采用室内试验、SEM电镜扫描等手段,结合Matlab多目标优化等方法,对掺加减水剂的缓凝型水泥浆液的锚固性能及配合比优化展开研究,得出适用于预应力锚杆自由段的注浆材料及其最优配合比,并与现行规范推荐配合比进行锚孔横断面结石特性对比试验。研究结果表明:1)随着水灰比增大,水泥浆液的流动度和凝结时间增大,体积结石率和抗压强度减小;随着减水剂掺量的增大,水泥浆液的流动度和凝结时间增大,体积结石率减小,减水剂对浆液抗压强度影响较小;2)未掺加减水剂时,浆液结石体致密性随着水灰比的增大而降低,掺加减水剂使得浆液结石体表面局部存在相对较大尺度的孔或孔隙,对宏观结石体强度有一定影响;3)通过Matlab多目标优化方法推荐了缓凝型水泥浆液最优配合比为水灰比0.3,减水剂掺量1.85%,相关性能参数符合规范要求,且流动度与抗压强度较规范推荐配合比分别提升了72.3%和107%;4)浸水围岩会弱化浆岩界面的抗剪强度,因此在锚杆灌浆过程中保证横断面结石率有利于提高浆岩界面的抗剪强度,本文提出的最优配合比浆液抗剪强度优于规范推荐配合比浆液。

层状反倾边坡破坏机制及NPR锚索控制效果物理模型试验

以内蒙古长山壕露天矿区大规模倾倒失稳反倾边坡为工程背景。首先基于相似理论构建层状反倾边坡地质概化物理模型,开展在未加固、普通锚索加固(PR锚索)及恒阻大变形锚索加固(NPR锚索)3种不同工况条件下边坡控制效果物理模型试验。然后使用红外热成像系统、应变监测系统和数字散斑位移测量系统,对反倾边坡开挖试验全过程的温度场、应变场和位移场进行综合监测。最后,研究层状反倾边坡变形特征和失稳机制,对比分析不同加固对策下的加固效果。研究结果表明:层状反倾边坡变形过程具有明显的"叠合悬臂梁"变形特征,其倾倒机制主要表现为岩层初始裂纹产生、岩层裂纹发育以及滑动面贯通边坡失稳3个阶段。PR锚索在边坡开挖过程中断裂失效,无法抵抗边坡大变形失稳。NPR锚索具有高恒阻、大变形以及吸收能量的超强特性,有效防止反倾边坡倾倒失稳的发生,为边坡工程加固提供了一种新的思路。

考虑永久位移的锚索框架减震锚头弹簧组件合理刚度研究

强震作用下预应力框架锚索可能出现内锚段松脱、锚索拉断等震害,在锚头处设置弹簧是一种新型抗震措施,而弹簧刚度的合理选取对改善锚索受力至关重要。建立在锚头处设置弹簧预应力锚索框架的加固基岩-覆盖层边坡三维数值模型,研究边坡在不同峰值加速度、不同持时地震波作用下响应规律,调整锚索-弹簧串联体系等效刚度大小,分析坡体永久位移和锚索轴力减载比随弹簧刚度的非线性变化特征;以控制边坡位移及锚索减载效果为目标,提出弹簧组件的合理刚度确定方法。研究表明:随弹簧刚度降低,缓冲减震作用逐渐显著;坡顶水平加速度受刚度变化影响较小,但当弹簧刚度低于临界值后边坡位移及弹簧变形量急剧增加;以边坡永久位移实际调查经验限值为首要控制条件,结合位移、弹簧峰值行程随刚度变化拟合“直-曲分界点”曲线,以共同确定弹簧刚度下限;同理,依据减载比拟合曲线轴力削减明显区段得出刚度上限,以保证一定工程经济性。针对算例模型取永久位移10 cm、拟合曲线曲率k小于0.002 k max作为直曲分界判断依据,得0.4 g~0.6g强震下弹簧刚度区间为(2.5,3.8)kN/mm,研究方法可为边坡预应力锚固工程抗震设计提供参考。